Digital band pass elliptic filter system

ABSTRACT

The filter coefficients of a digital band pass elliptic filter can be approximated to a linear function of the center frequency of the pass band width. The filter coefficients of a band pass digital filter having a predetermined center frequency and the slope of this linear function are stored in first and second memories. A central processing unit (CPU) obtains the difference between a desired center frequency and a predetermined center frequency. A multiplier multiplies the slope stored in the second memory by the difference obtained by the CPU. An adder adds each of the filter coefficients stored in the first memory to an associated one of the products output from the multiplier. The adding results become the filter coefficients for obtaining the desired center frequency. Those filter coefficients are set in a digital filter.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a digital filter, and, moreparticularly, to a digital band pass elliptic filter capable of changingthe center frequency of a pass band and/or the pass band width.

2. Description of the Related Art

Digital band pass filters are used in various technical fields.

For example, Japanese Unexamined Patent Publication No. 16573/1980discloses an infinite impulse response (IIR) variable digital filterwhich can independently alter the center frequency of its pass band andthe width of the pass band.

The IIR variable digital filter described in this publication changesthe center frequency and the pass band width in the following manner.

First, with P=jΩ=j2πf, the transfer function H_(L) (P) of a low-passfilter (LPF) on the P plane is expressed by an equation (1) below.

    H.sub.L (P)=(a.sub.O P.sup.2 +a.sub.1 P+a.sub.2)/(P.sup.2 +b.sub.1 P+b.sub.2)                                                (1)

The transfer function of the band pass filter can be obtained bytransforming the transfer function H_(L) (P) along the frequency axisaccording to the following equation (2).

    P→B.sub.O (P+Ω.sub.O.sup.2 /P)                (2)

where B₀ is the pass band width and Ω_(O) is the center frequency.

From the equations (1) and (2), the transfer function H_(B) (P) of theband pass filter becomes as expressed by an equation (3). ##EQU1##

The transfer function on the Z plane, when acquired by thetransformation given by the following equation (4), becomes as expressedby an equation (5) below.

    P→(1-Z.sup.-2)/(2Z.sup.-1)                          (4) ##EQU2##

In the equation (5), Φ(Z, Ω_(O) ²)/B₀ is the function of the pass bandwidth and center frequency of the filter. By acquiring Φ(Z, Ω_(O) ²)/B₀from the desired (target) center frequency and the pass band width andsubstituting the result in the equation (5), the transfer function ofthe desired band pass filter can be obtained.

For the IIR variable digital filter disclosed in Japanese UnexaminedPatent Publication No. 16573/1980, however, the value of the functionΦ(Z, Ω_(O) ²)/B₀ should be obtained to alter the center frequency of thepass band and pass band width.

Φ(Z, Ω_(O) ²)/B₀ is a non-linear function of the center frequency andthe pass band width and its computation is complex involving a vastamount of calculations, resulting in a long computation time and a largerounding error. Further, to store the transfer function and execute thecomputation, a large memory capacity is disadvantageously needed.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a digitalband pass elliptic filter which can alter the center frequency and/orpass band width with a less amount of computation and a smaller memorycapacity.

To achieve the above object, according to one aspect of this invention,there is provided a center-frequency variable type digital band passelliptic filter system comprising:

an N-order digital band pass elliptic filter for filtering an inputdigital signal in accordance with filter coefficients {a_(1i), a_(2i),b_(1i) } (i=1, 2, . . . , N/2; N being an even);

memory means for storing linear coefficients k_(aji) and k_(bli)computed according to following equations, using filter coefficients{a_(1i) (f_(a)), a_(2i) (f_(a)), b_(1i) (f_(a))} and {a_(1i) (f_(b)),a_(2i) (f_(b)), b_(1i) (f_(b))} of first and second known digital bandpass elliptic filters having a same pass band width and pass band centerfrequencies f_(a) and f_(b), and filter coefficients {(a_(1i) (f_(r)),a_(2i) (f_(r)), b_(1i) (f_(r))} of a third known digital band passelliptic filter having the same pass band width as that of the first andsecond known digital band pass elliptic filters and a pass band centerfrequency fr,

    k.sub.aji =[a.sub.ji (f.sub.b)-a.sub.ji (f.sub.a)]/(f.sub.b -f.sub.a)

i=1, 2, . . . , N/2, j=1, 2

    k.sub.b1i =[b.sub.1i (f.sub.b)-b.sub.1i (f.sub.a)]/(f.sub.b -f.sub.a)

i=1, 2, . . . , N/2;

shift-amount setting means for setting a shift amount mΔf between adesired center frequency of the N-order digital band pass ellipticfilter and a predetermined center frequency f_(r) ;

multiplying means for multiplying the shift amount mΔf, supplied fromthe shift-amount setting means, by each of the linear coefficientsK_(aji) and k_(b1i) to yield mΔf.k_(aji) and mΔf.k_(b1i) ;

adding means for adding each of products obtained by the multiplyingmeans to an associated one of the filter coefficients stored in thememory means to obtain a_(1i) (f_(r)) mΔf.k_(a1i), a_(2i)(f_(r))+mΔf.k_(a2i) and b_(1i) (f_(r))+mΔf.k_(b1i) ; and

setting means for setting values a_(1i) (f_(r))+mΔf.k_(a1i), a_(2i)(f_(r))+mΔf.k_(a2i) and b_(1i) (f_(r))+mΔf.k_(b1i) obtained by theadding means as the filter coefficients {a_(1i), a_(2i), b_(1i) } of theN-order digital band pass elliptic filter, thereby setting a centerfrequency of the N-order digital band pass elliptic filter to f_(r)+mΔf.

As the predetermined center frequency f_(r), the center frequenciesf_(a) and f_(b) of known digital band pass elliptic filters may be used.

According to another aspect of this invention, there is provided aband-width variable type digital band pass elliptic filter systemcomprising:

an N-order digital band pass elliptic filter for filtering an inputdigital signal in accordance with filter coefficients {a_(1i), a_(2i),b_(1i) } (i=1, 2, . . . , N/2; N being an even);

memory means for storing linear coefficients k_(aji) and k_(b1i)computed according to following equations, using filter coefficients{a_(1i) (B_(a)), a_(2i) (B_(a)), b_(1i) (B_(a))} and {a_(1i) (B_(b)),a_(2i) (B_(b)), b_(1i) (B_(b))} of first and second known digital bandpass elliptic filters having a same center frequency and pass bandwidths B_(a) and B_(b), and filter coefficients {a_(1i) (B_(r)), a_(2i)(B_(r)), b_(1i) (B_(r))} of a third known digital band pass ellipticfilter having the same center frequency as that of the first and secondknown digital band pass elliptic filters and a pass band width Br,

    k.sub.aji =[a.sub.ji (B.sub.b)-a.sub.ji (B.sub.a)]/(B.sub.b -B.sub.a)

i=1, 2, . . . , N/2, j=1, 2

    k.sub.b1i =[b.sub.1i (B.sub.b)-b.sub.1i (B.sub.a)]/(B.sub.b -B.sub.a)

i=1, 2, . . . , N/2;

shift-amount setting means for setting a shift amount mΔB between adesired pass band width of the N-order digital band pass elliptic filterand a predetermined pass band width B_(r) ;

multiplying means for multiplying the shift amount mΔB, supplied fromthe shift-amount setting means, by each of the linear coefficientsK_(aji) and k_(b1i) to yield mΔB.k_(aji) and mΔB.k_(b1i) ;

adding means for adding each of products obtained by the multiplyingmeans to an associated one of the filter coefficients stored in thememory means to obtain a_(1i) (B_(r))+mΔB.k_(a1i), a_(2i)(B_(r))+mΔB.k_(a2i) and b_(1i) (B_(r))+mΔB.k_(b1i) ; and

setting means for setting values a_(1i) (B_(r))+mΔB.k_(a1i), a_(2i)(B_(r))+mΔB.k_(a2i) and b_(1i) (B_(r))+mΔB.k_(b1i) obtained by theadding means as the filter coefficients {a_(1i), a_(2i), b_(1i) } of theN-order digital band pass elliptic filter, thereby setting a pass bandwidth of the N-order digital band pass elliptic filter to B_(r) +mΔB.

As the predetermined pass band width B_(r), the pass band widths B_(a)and B_(b) of known digital band pass elliptic filters may be used.

The filter coefficients {a_(1i), a_(2i), b_(1i) } of an N-order digitalband pass elliptic filter can be substantially approximated by linearfunctions of the center frequency and pass band width. With theabove-described structures, therefore, filter coefficients, when thedesired center frequency or desired pass band width is obtained, can beacquired with a smaller amount of computation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating the basic structure of an N-order IIRdigital band pass elliptic filter;

FIG. 2 is a block diagram showing the structure of a digital filtersystem embodying the present invention;

FIGS. 3 to 5 are graphs of linear functions of filter coefficients of adigital filter system according to a first embodiment of this invention;

FIG. 6 is a graph exemplifying a change in the center frequency of thepass band of the digital filter system according to the first embodimentof this invention;

FIG. 7 is a block diagram showing a modification of the structure of thedigital filter system embodying the present invention;

FIGS. 8 to 10 are graphs of linear functions of filter coefficients of adigital filter system according to a second embodiment of thisinvention; and

FIG. 11 is a graph exemplifying a change in the width of the pass bandof the digital filter system according to the second embodiment of thisinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The structure of a digital band pass elliptic filter system according topreferred embodiments of the present invention will be described belowwith reference to the accompanying drawings. In the followingdescription, a frequency is expressed in the form of normalized one.

First Embodiment

First, an N-order IIR digital band pass elliptic filter system of acenter-frequency variable type according to the first embodiment will bediscussed from the theoretical aspect, and then its specific circuitstructure will be explained.

FIG. 1 illustrates an example of an N-order IIR digital band passelliptic filter having N/2 two-order IIR filter sections connected in acascade form. For the digital band pass elliptic filter having thestructure shown in FIG. 1, a filter coefficient b₂₁ is almost "1."

Thus, its transfer function is approximately expressed by an equation(6). ##EQU3##

Given that the pass band width (the width of the pass band) is constant,individual filter coefficients a_(1i), a_(2i) and bli in the equation(6) approximately become linear functions of a normalized centerfrequency of the pass band (center frequency of the pass band with thesampling frequency taken as "1").

Thus, the transfer function in the equation (6) can be rewritten as anequation (7). ##EQU4## where f_(c) is the normalized center frequency(0<f_(c) <0.5) of the pass band, i.e., the center frequency with thesampling frequency taken as "1," and a_(1i) (f_(c)), a_(2i) (f_(c)) andb_(1i) (f_(c)) indicate that the filter coefficients a_(1i), a_(2i) andb_(1i) are linear functions of the normalized center frequency f_(c).

If the pass band width of this band pass digital filter is Δf_(B) andthe normalized center frequency f_(c) changes from f₁ to f₂,

    0<f.sub.1 <f.sub.2 <0.5, 0<f.sub.1 -Δf.sub.B /2, and

    f.sub.2 +Δf.sub.B /2<0.5

are satisfied.

As the filter coefficients a_(1i) (f_(c)), a_(2i) (f_(c)) and b_(1i)(f_(c)) are linear functions of the center frequency f_(c), the valuesof the filter coefficients change in accordance with the amount of achange in center frequency f_(c). Therefore, if the amount of a changein each filter coefficient with respect to a unit amount of a change Δfof the center frequency f_(c) (=the slope of a linear function of eachfilter coefficient)is obtained previously and the slope is multiplied bythe amount of a change (shift amount) from the reference value of thecenter frequency f_(c), it is possible to acquire the amount of a changein each filter coefficient for changing the center frequency f_(c) fromthe reference value. By adding the acquired change amount to the filtercoefficients when the reference value of the center frequency f_(c) isobtained, filter coefficients necessary for attaining an arbitrarycenter frequency f_(c) can be obtained.

According to this embodiment, therefore, the slope of the linearequation of each filter coefficient is obtained using the filtercoefficients of arbitrary two known N-order IIR band pass digitalfilters. For example, provided that the two filters respectively havingthe center frequencies f_(a) and f_(b) (=f_(a) +nΔf) have filtercoefficients {a_(1i) (f_(a)), a_(2i) (f_(a)), b_(1i) (f_(a))} and{a_(1i) (f_(b), a_(2i) (f_(b), b_(1i) (f_(b))}, the slopes of the linearequations can be obtained from equations (8) to (10).

    k.sub.a1i =[a.sub.1i (f.sub.b)-a.sub.1i (f.sub.a)]/(f.sub.b -f.sub.a)(8)

i=1, 2, . . . , N/2

    k.sub.a2i =[a.sub.2i (f.sub.b)-a.sub.2i (f.sub.a)]/(f.sub.b -f.sub.a)(9)

i=1, 2, . . . , N/2

    k.sub.b1i =[b.sub.1i (f.sub.b)-b.sub.1i (f.sub.a)]/(f.sub.b -f.sub.a)(10)

i=1, 2, . . . , N/2

The linear equations of the individual filter coefficients are obtainedfrom equations (11) to (13) using the acquired slopes and the centerfrequency of another arbitrary known band pass digital filter, which hasthe same pass band width as the aforementioned two known band passdigital filters, e.g., a band pass digital filter having a centerfrequency f_(r).

    a.sub.1i (f)=k.sub.a1i ·(f-f.sub.r)+a.sub.1i (f.sub.r)(11)

    a.sub.2i (f)=k.sub.a2i ·(f-f.sub.r)+a.sub.2i (f.sub.r)(12)

    b.sub.1i (f)=k.sub.b1i ·(f-f.sub.r)+b.sub.1i (f.sub.r)(13)

where f is the desired center frequency from which the individual filtercoefficients can be obtained. By setting the obtained filtercoefficients as new filter coefficients, the band pass digital filterhaving the desired center frequency is obtained.

If the center frequency f_(r) is set equal to the aforementioned centerfrequency f_(a) or f_(b), for example, the filter coefficients used inthe equation (8) to (10) can also be used.

With f_(r) +f_(a), for instance, the equations (11) to (13) will berewritten as equations (14) to (16), respectively.

    a.sub.1i (f)=k.sub.a1i ·(f-f.sub.a)+a.sub.1i (f.sub.a)(14)

    a.sub.2i (f)=k.sub.a2i ·(f-f.sub.a)+a.sub.2i (f.sub.a)(15)

    b.sub.1i (f)=k.sub.bli ·(f-f.sub.a)+b.sub.1i (f.sub.a)(16)

The structure of a digital filter system which can alter the centerfrequency using the above-described scheme will now be explained withreference to FIG. 2.

As shown in FIG. 2, this digital filter system comprises a CPU 11, afirst memory 13, a second memory 15, a multiplier 17, an adder 19, anN-order IIR digital band pass elliptic filter 21, and a shift knob SV.

A user should manipulates a shift knob SV to instruct the desired centerfrequency of the pass band width of the digital filter system to the CPU11.

The CPU 11 controls the general operation of this digital filter systemand supplies the amount of a shift from the reference value of thecenter frequency (shift amount), mΔf, to the multiplier 17 in accordancewith the instruction from the shift knob SV. The center frequency ischanged in the units of Δf, m indicating the number of steps.

The first memory 13 stores the filter coefficients {a_(1i) (f_(a)),a_(2i) (f_(a)), b_(1i) (f_(a))} of the aforementioned arbitrary knowndigital band pass elliptic filters.

The second memory 15 stores the aforementioned slopes., k_(a1i), k_(a2i)and k_(b1i) (i=1, 2, . . . , N/2).

The multiplier 17 obtains the products of the shift amount mΔf of thepass band center frequency supplied from the CPU 11 and the slopesk_(a1i), k_(a2i) and k_(b1i) stored in the second memory 15, k_(ali)·mΔf, k_(a2i) ·mΔf and k_(b1i) ·mΔf, i.e., the change amounts of thefilter coefficients due to a shift in center frequency.

The adder 19 adds each of the filter coefficients a_(1i) (f_(a)), a_(2i)(f_(a)), b_(1i) (f_(a)) stored in the first memory 13, to an associatedone of the multiplication results from the multiplier 17, k_(a1i) ·mΔf,k_(a2i) ·mΔf and k_(b1i) ·mΔf, to attain new filter coefficients.

The digital band pass elliptic filter 21, which has a structure as shownin FIG. 1, for example, filters an input digital signal in accordancewith the filter coefficients supplied from the adder 19. The digitalsignal supplied to the digital band pass elliptic filter may be obtainedthrough A/D conversion of an analog acoustic signal at an arbitrarysampling period. A digital signal output from the digital band passelliptic filter 21 is supplied to an analog circuit in the subsequentstage after being subjected to, for example, D/A conversion.

A specific description will now be given of an example of designing aneight-order center-frequency variable digital band pass elliptic filterwhich has a normalized pass band width of 0.025 with a unit changeamount of the center frequency being 0.005.

Assume that the filter coefficients of known band pass digital filtersFA and FB having a normalized pass band width of 0.025 take thefollowing values.

For band pass digital filter FA,

normalized center frequency f_(ca) =0.275

    a.sub.11 =0.1349, a.sub.12 =0.4758, a.sub.13 =0.2274, a.sub.14 =0.3692,

    a.sub.21 =0.9605, a.sub.22 =0.9616, a.sub.23 =0.9030, a.sub.24 =0.9041,

    b.sub.11 =-1.1288, b.sub.12 =-0.4022, b.sub.13 =-1.4847, b.sub.14 =-0.9559.

For band pass digital filter FB,

normalized center frequency f_(cb) =0.285

    a.sub.11 =0.1962, a.sub.12 =0.5354, a.sub.13 =0.2868, a.sub.14 =0.4278,

    a.sub.21 =0.9604, a.sub.22 =0.9617, a.sub.23 =0.9029, a.sub.24 =0.9043,

    b.sub.11 =-1.0896, b.sub.12 =-0.3442, b.sub.13 =1.5159, b.sub.14 =1.0074.

In this case, the first memory 13 stores the individual filtercoefficients of one of the band pass digital filters FA and FB, e.g.,those of the filter FA.

The slopes of the linear functions of the individual filter coefficientsare expressed as follows.

    k.sub.a1i =[a.sub.1i (f.sub.cb)-a.sub.1i (f.sub.ca)]/(f.sub.cb -f.sub.ca)

    k.sub.a2i =[a.sub.2i (f.sub.cb)-a.sub.2i (f.sub.ca)]/(f.sub.cb -f.sub.ca)

    k.sub.b1i =[b.sub.1i (f.sub.cb)-b.sub.1i (f.sub.ca)]/(f.sub.cb -f.sub.ca)

    f.sub.cb -f.sub.ca =0.01

The individual slopes take the following values.

    k.sub.a11 =6.1300, k.sub.a12 =5.9600, k.sub.a13 =5.9400, k.sub.a14 =5.8600,

    k.sub.a21 =-0.0100, k.sub.a22 =0.0100, k.sub.a23 =0.0100, k.sub.a24 =0.0200,

    k.sub.b11 =3.9200, k.sub.b12 =5.8000, k.sub.b13 =3.1200, k.sub.b14 =5.1500.

Those values are stored in the second memory 15.

When the CPU 11 outputs the difference mΔf (=f-f_(ca)) between thereference center frequency f_(ca) and the desired center frequency findicated by the shift knob SV, the multiplier 17 obtains the product ofeach slope and the frequency difference mΔf.

    k.sub.a11 ·mΔf=6.1300·mΔf, k.sub.a12 ·mΔf=5.9600·mΔf,

    k.sub.a13 ·mΔf=5.9400·mΔf, k.sub.a14 ·mΔf=5.8600·mΔf,

    k.sub.a21 ·mΔf=-0.0100·mΔf, k.sub.a22 ·mΔf=0.0100·mΔf,

    k.sub.a23 ·mΔf=-0.0100·mΔf, k.sub.a24 ·mΔf=0.0200·mΔf,

    k.sub.b11 ·mΔf=3.9200·mΔf, k.sub.b12 ·mΔf=5.8000·mΔf,

    k.sub.b13 ·mΔf=3.1200·mΔf, k.sub.b14 ·mΔf=5.1500·mΔf.

Upon reception of the multiplication results from the multiplier 17, theadder 19 adds each of the filter coefficients stored in the first memory13 to an associated one of the received products to yield new filtercoefficients.

    a.sub.11 '=k.sub.a11 ·mΔf+a.sub.11 (f.sub.ca)=6.1300·mΔf+0.1349,

    a.sub.12 '=k.sub.a12 ·mΔf+a.sub.12 (f.sub.ca)=5.9600·mΔf+0.4758,

    a.sub.13 '=k.sub.a13 ·mΔf+a.sub.13 (f.sub.ca)=5.9400·mΔf+0.2274,

    a.sub.14 '=k.sub.a14 ·mΔf+a.sub.14 (f.sub.ca)=5.8600·mΔf+0.3692,

    a.sub.21 '=k.sub.a21 ·mΔf+a.sub.21 (f.sub.ca)=-0.0100·mΔf+0.9605,

    a.sub.22 '=k.sub.a22 ·mΔf+a.sub.22 (f.sub.ca)=0.0100·mΔf+0.9616,

    a.sub.23 '=k.sub.a23 ·mΔf+a.sub.23 (f.sub.ca)=-0.0100·mΔf+0.9030,

    a.sub.24 '=k.sub.a24 ·mΔf+a.sub.24 (f.sub.ca)=0.0200·mΔf+0.9041,

    b.sub.11 '=k.sub.b11 ·mΔf+b.sub.11 (f.sub.ca)=3.9200·mΔf-1.1288,

    b.sub.12 '=k.sub.b12 ·mΔf+b.sub.12 (f.sub.ca)=5.8000·mΔf-0.4022,

    b.sub.13 '=k.sub.b13 ·mΔf+b.sub.13 (f.sub.ca)=3.1200·mΔf+1.4847,

    b.sub.14 '=k.sub.b14 ·mΔf+b.sub.14 (f.sub.ca)=5.1500·mΔf+0.9559.

The digital band pass elliptic filter 21 receives the filtercoefficients a₁₁ ', a₁₂ ', a₁₃ ', a₁₄ ', a₂₁ ', a₂₂ ', a₂₃ ', a₂₄ ', b₁₁', b₁₂ ', b₁₃ ', and b₁₄ ' from the adder 19, and sets them as newfilter coefficients therein, and filters the input digital signal inaccordance with the received filter coefficients and outputs thefiltered digital signal.

FIGS. 3 through 5 show the relationships between the thus obtainedindividual filter coefficients and the shift amount mΔf, and FIG. 6shows an example of the characteristic of the digital band pass ellipticfilter system.

In FIG. 6, the center frequency changes with a fixed band width. Namely,the digital band pass elliptic filter system of this example has a fixednormalized band width of 0.025 and a variable center frequency.

According to this embodiment, as described above, for an eight-order IIRdigital band pass elliptic filter, for example, new filter coefficientscan be obtained through 12 multiplications by the multiplier 17 and 12additions by the adder 19. This embodiment can therefore change thecenter frequency with a smaller amount of computation as compared withthe prior art. The fewer calculations result in fewer computationerrors. As the first and second memories 13 and 15 merely store 24pieces of data, they can have a small capacity.

Although the foregoing description has been given with reference to thecase where the first and second memories 13 and 15, the multiplier 17,the adder 19 and the digital band pass elliptic filter 21 areconstituted of separate hardware, those components may be constituted ofan ordinary DSP (Digital Signal Processor) as shown in FIG. 7.

Although the foregoing description has explained that the CPU 11 outputsthe difference mΔf between the center frequency f_(a) of one (FA) of thetwo known digital band pass elliptic filters FA and FB (reference centerfrequency) and the desired center frequency f, the CPU 11 may output thedesired center frequency f and another circuit may compute thedifference mΔf between the desired center frequency and the referencecenter frequency f_(a) and supply the difference to the multiplier 17.

Second Embodiment

The foregoing description of the first embodiment has explained that thecenter frequency is changed without altering the pass band width.However, this invention is also applicable to an N-order IIR digitalband pass elliptic filter system which can change the pass band width(the width of the pass band) without changing the center frequency. Thefollowing describes such an IIR digital band pass elliptic filter systemwhich can change the pass band width as a second embodiment.

Given that the center frequency of the band pass is constant, theindividual filter coefficients a_(1i), a_(2i) and b_(1i) in the equation(6) approximately become linear functions of a pass band width B.

Thus, the transfer function in the equation (6) can be rewritten as anequation (17). ##EQU5## where B₀ is the normalized pass band width,i.e., the pass band width with the sampling frequency of the inputdigital signal taken as "1," and a_(1i) (B₀), a_(2i) (B₀) and b_(1i)(B₀) indicate that the filter coefficients a_(1i), a_(2i) and b_(1i) arelinear functions of the pass band width B₀.

If the center frequency of this digital filter is f_(c) and the passband width B₀ changes from B₁ to B₂,

    0<B.sub.1 <B.sub.2 <0.5, 0<f.sub.c -B.sub.2 /2, and

    f.sub.c +B.sub.2 /2<0.5

are satisfied.

As the filter coefficients a_(1i), a_(2i) and b_(1i) are linearfunctions of the normalized pass band width B₀, the values of thosefilter coefficients change in accordance with the amount of a change,mΔB, in normalized pass band width B₀. Therefore, if the amount of achange in each filter coefficient with respect to a unit amount of achange ΔB of the normalized pass band width, i.e., the slope of thelinear function of each filter coefficient, is obtained previously andthe slope is multiplied by the amount of a change in pass band width,mΔB, it is possible to acquire the amount of a change in each filtercoefficient for changing the pass band width. By adding the acquiredchange amount of each filter coefficient to the reference filtercoefficient, filter coefficients necessary for attaining that pass bandwidth can be obtained.

According to the second embodiment, therefore, the slope of the linearequation of each filter coefficient is obtained using the filtercoefficients of two known digital filters which have the same centerfrequency but different pass band widths. For example, provided that thetwo filters respectively having the pass band widths B_(a) and B_(b)have filter coefficients {a_(1i) (B_(a)), a_(2i) (B_(a)), b_(1i)(B_(a))} and {a_(1i) (B_(b)), a_(2i) (B_(b)), b_(1i) (B_(b))}, theslopes of the linear equations can be obtained from equations (18) to(20).

    k.sub.a1i =[a.sub.1i (B.sub.b)-a.sub.1i (B.sub.a)]/(B.sub.b -B.sub.a)(18)

i=1, 2, . . . , N/2

    k.sub.a2i =[a.sub.2i (B.sub.b)-a.sub.2i (B.sub.a)]/(B.sub.b -B.sub.a)(19)

i=1, 2, . . . , N/2

    k.sub.b1i =[b.sub.1i (B.sub.b)-b.sub.1i (B.sub.a)]/(B.sub.b -B.sub.a)(20)

i=1, 2, . . . , N/2

The linear equations of the individual filter coefficients are obtainedfrom equations (21) to (23) using the acquired slopes and the filtercoefficients of another arbitrary known digital filter, which has thesame center frequency as the aforementioned two known digital filtersand has a pass band width B_(r).

    a.sub.1i (B)=k.sub.a1i ·(B-B.sub.r)+a.sub.1i (B.sub.r)(21)

    a.sub.2i (B)=k.sub.a2i ·(B-B.sub.r)+a.sub.2i (B.sub.r)(22)

    b.sub.1i (B)=k.sub.b1i ·(B-B.sub.r)+b.sub.1i (B.sub.r)(23)

where B is the normalized pass band width of the digital filter to beobtained. By setting the obtained filter coefficients in the digitalfilter, the digital band pass elliptic filter, which has the same centerfrequency as that of the known digital filters and the normalized passband width B.

If the pass band width B_(r) is set equal to the aforementioned passband width B_(a) or B_(b), for example, the filter coefficients used inthe equation (18) to (20) can also be used.

The specific structure and operation of this digital band pass ellipticfilter system will now be described.

The structure is the same as that of the first embodiment shown in FIG.2.

In this embodiment, the knob SV is used to input an instruction to widenor narrow the pass band width. The CPU 11 controls the general operationof this digital filter system and supplies the difference mΔB betweenthe desired pass band width B and the reference pass band width B_(a) tothe multiplier 17 in accordance with the manipulation of the knob SV.

The first memory 13 stores the filter coefficients {a_(1i) (B_(a)),a_(2i) (B_(a)), b_(1i) (B_(a))} of the aforementioned arbitrary knowndigital filters.

The second memory 15 stores slopes k_(a1i), k_(a2i) and k_(b1i) (i=1, 2,. . . , N/2), which have been computed in advance.

The multiplier 17 obtains the difference mΔB output from the CPU 11 andthe slopes k_(a1i), k_(a2i) and k_(b1i) stored in the second memory 15,k_(a1i) ·mΔB, k_(a2i) ·mΔB and k_(b1i) ·mΔB, i.e., the change amounts ofthe filter coefficients due to a variation in pass band width.

The adder 19 adds each of the filter coefficients a_(1i) (B_(a)), a_(2i)(B_(a)), b_(1i) (B_(a)) stored in the first memory 13, to an associatedone of the multiplication results from the multiplier 17, k_(a1i) ·mΔB,k_(a2i) ·mΔB and k_(b1i) ·mΔB, to attain new filter coefficients.

The digital band pass elliptic filter 21 filters the input digitalsignal in accordance with the filter coefficients supplied from theadder 19.

In this manner, the IIR digital band pass elliptic filter which canchange the pass band width as needed is obtained.

The first and second memories 13 and 15, the multiplier 17, the adder 19and the digital band pass elliptic filter 21 may be constituted of adigital signal processor (DSP) as shown in FIG. 7.

A specific description will now be given of an example of designing aneight-order digital band pass elliptic filter which has a normalizedcenter frequency of 0.25 with a unit change amount of the pass bandwidth being 0.001.

Assume that the filter coefficients and pass band widths of known bandpass digital filters FC and FD having a normalized center frequency of0.25 take the following values.

For band pass digital filter FC,

normalized pass band width B_(c) =0.016

    a.sub.11 =0.1113, a.sub.12 =-0.113, a.sub.13 =0.0466, a.sub.14 =-0.0466,

    a.sub.21 =0.9748, a.sub.22 =0.9748, a.sub.23 =0.9372, a.sub.24 =0.9372,

    b.sub.11 =1.0208, b.sub.12 =-1.0208, b.sub.13 =0.4819, b.sub.14 =-0.4819.

For band pass digital filter FD, normalized pass band width B_(d) =0.018

    a.sub.11 =0.1250, a.sub.12 =-0.1250, a.sub.13 =0.0522, a.sub.14 =-0.0522,

    a.sub.21 =0.9717, a.sub.22 =0.9717,a.sub.23 =0.9297, a.sub.24 =0.9297,

    b.sub.11 =1.1077, b.sub.12 =-1.1077, b.sub.13 =0.5351, b.sub.14 =-0.5351.

In this case, the first memory 13 stores the individual filtercoefficients of one of the band pass digital filters FC and FD, e.g.,those of the filter FC.

The slopes of the linear functions of the individual filter coefficientsare expressed as follows.

    k.sub.a1i =[a.sub.1i (B.sub.d)-a.sub.1i (B.sub.c)]/(B.sub.d -B.sub.c)

    k.sub.a2i =[a.sub.2i (B.sub.d)-a.sub.2i (B.sub.c)]/(B.sub.d -B.sub.c)

    k.sub.b1i =[b.sub.1i (B.sub.d)-b.sub.1i (B.sub.c)]/(B.sub.d -B.sub.c)

    B.sub.d -B.sub.c =0.002

The individual slopes take the following values.

    k.sub.a11 =6.8500, k.sub.a12 =-6.8500, k.sub.a13 =2.8000, k.sub.a14 =-2.8000,

    k.sub.a21 =-1.5500, k.sub.a22 =-1.5500, k.sub.a23 =-3.7500, k.sub.a24 =-3.7500,

    k.sub.b11 =43.4500, k.sub.b12 =-43.4500, k.sub.b13 =26.6000, k.sub.b14 =-26.6000.

Those values are stored in the second memory 15.

When the CPU 11 outputs the difference mΔB (=B-B_(c) =B-0.016) betweenthe reference pass band width B_(c) and the desired pass band width Bindicated by the shift knob SV, the multiplier 17 obtains the product ofeach slope and the frequency difference mΔB.

    k.sub.a11 ·mΔB=6.8500·mΔB, k.sub.a12 ·mΔB=-6.8500·mΔB,

    k.sub.a13 ·mΔB=2.8000·mΔB, k.sub.a14 ·mΔB=-2.8000·mΔB,

    k.sub.a21 ·mΔB=-1.5500·mΔB, k.sub.a22 ·mΔB=-1.5500·mΔB,

    k.sub.a23 ·mΔB=-3.7500·mΔB, k.sub.a24 ·mΔB=-3.7500·mΔB,

    k.sub.b11 ·mΔB=43.4500·mΔB, k.sub.b12 ·mΔB=-43.4500·mΔB,

    k.sub.b13 ·mΔB=26.6000·mΔB, k.sub.b14 ·mΔB=-26.6000·mΔB.

Upon reception of the multiplication results from the multiplier 17, theadder 19 adds each of the filter coefficients stored in the first memory13 to an associated one of the received products to yield new filtercoefficients.

    a.sub.11 '=k.sub.a11 ·mΔB+a.sub.11 (B.sub.c)=6.8500·mΔB+0.1113,

    a.sub.12 '=k.sub.a12 ·mΔB+a.sub.12 (B.sub.c)=-6.8500·mΔf-0.1113,

    a.sub.13 '=k.sub.a13 ·mΔB+a.sub.13 (B.sub.c)=2.8000·mΔf+0.0466,

    a.sub.14 '=k.sub.a14 ·mΔB+a.sub.13 (B.sub.c)=-2.8000·mΔf-0.0466,

    a.sub.21 '=k.sub.a21 ·mΔB+a.sub.21 (B.sub.c)=-1.5500·mΔf+0.9748,

    a.sub.22 '=k.sub.a22 ·mΔB+a.sub.22 (B.sub.c)=-1.5500·mΔf+0.9748,

    a.sub.23 '=k.sub.a23 ·mΔB+a.sub.23 (B.sub.c)=-3.7500·mΔf+0.9372,

    a.sub.24 '=k.sub.a24 ·mΔB+a.sub.24 (B.sub.c)=-3.7500·mΔf+0.9372,

    b.sub.11 '=k.sub.b11 ·mΔB+b.sub.11 (B.sub.c)=43.4500·mΔf+1.0208,

    b.sub.12 '=k.sub.b12 ·mΔB+b.sub.12 (B.sub.c)=-43.4500·mΔf+1.0208,

    b.sub.13 '=k.sub.b13 ·mΔB+b.sub.13 (B.sub.c)=26.6000·mΔf+0.4819,

    b.sub.14 '=k.sub.b14 ·mΔB+b.sub.14 (B.sub.c)=-26.6000·mΔf+0.4819.

The digital band pass elliptic filter 21 receives the filtercoefficients a₁₁ ', a₁₂ ', a₁₃ ', a₁₄ ', a₂₁ ', a₂₂ ', a₂₃ ', a₂₄ ', b₁₁', b₁₂ ', b₁₃ ', and b₁₄ ' from the adder 19, filters the input digitalsignal in accordance with the received filter coefficients and outputsthe filtered digital signal.

FIGS. 8 through 10 show the relationships between the thus obtainedindividual filter coefficients and the shift amount mΔB, and FIG. 11shows an example of the characteristic of the digital band pass ellipticfilter system.

As can be understood from FIG. 11, the digital band pass elliptic filtersystem of this example has the fixed normalized center frequency of 0.25and variable pass band width.

According to the second embodiment, as described above, for aneight-order digital band pass elliptic filter, for example, new filtercoefficients can be obtained through 12 multiplications by themultiplier 17 and 12 additions by the adder 19, thus allowing the passband width to be changed with a smaller amount of computation ascompared with the prior art. The fewer calculations result in fewercomputation errors. As the first and second memories 13 and 15 merelystore 24 pieces of data, they can have a small capacity.

Although the foregoing description has been given with reference to thecase where the first and second memories 13 and 15, the multiplier 17,the adder 19 and the digital band pass elliptic filter 21 areconstituted of separate components, those components may be constitutedof an ordinary DSP and a CPU which gives necessary instructions to theDSP, as shown in FIG. 7.

Although the foregoing description has explained that the CPU 11 outputsthe difference mΔB between the pass band width B_(a) of one of the twoknown digital filters (reference pass band width) and the desired passband width B, the CPU 11 may output the desired pass band width B andanother circuit may compute the difference mΔB between the desired passband width B and the reference pass band width B_(a) and supply thedifference to the multiplier 17.

The pass band width is fixed in the first embodiment, whereas the centerfrequency is fixed in the second embodiment. This invention can howeverchange the center frequency and pass band width simultaneously.

In this case, the filter coefficients of two known digital filtersshould be prepared for each combination of the pass band width andcenter frequency, the slopes should be computed and stored in the secondmemory 15 for each combination of the pass band width and centerfrequency, and the reference filter coefficient should be stored in thefirst memory 13 for each combination of the pass band width and centerfrequency. The proper slope and filter coefficients are read inaccordance with the combination of the center frequency and pass bandwidth output from the CPU 11, and new filter coefficients are obtainedbased on those read data to set the desired digital filter.

The present invention is not limited to the above-described embodiments,but may be modified and applied in various other forms and manners.

In short, according to the present invention, the filter coefficientsfor obtaining the desired center frequency and desired pass band widthcan be acquired with a smaller memory capacity and fewer computations,and the desired center frequency and pass band width can be obtainedrelatively easily based on the acquired filter coefficients.

What is claimed is:
 1. A center-frequency variable type digital bandpass elliptic filter system comprising:an N-order digital band passelliptic filter for filtering an input digital signal in accordance withfilter coefficients {a_(1i), a_(2i), b_(li) } (i=1, 2, . . . , N/2; Nbeing an even); memory means for storing linear coefficients k_(aji) andk_(b1i) computed according to following equations, using filtercoefficients {a_(1i) (f_(a)), a_(2i) (f_(a)), b_(1i) (f_(a))} and{a_(1i) (f_(b)), a_(2i) (f_(b)), b_(1i) (f_(b))} of first and secondknown digital band pass elliptic filters having a same pass band widthand the pass band center frequencies f_(a) and f_(b), and for storingfilter coefficients {a_(1i) (f_(r)), a_(2i) (f_(r)), b_(1i) (f_(r))} ofa third known digital band pass elliptic filter having the same passband width as that of said first and second known digital band passelliptic filters and a pass band center frequency fr,

    k.sub.aji ={a.sub.ji (f.sub.b)-a.sub.ji (f.sub.a)}/(f.sub.b -f.sub.a)

i=1, 2, . . . , N/2, j=1, 2

    k.sub.b1i ={b.sub.1i (f.sub.b)-b.sub.1i (f.sub.a)}/(f.sub.b -f.sub.a)

i=1, 2, . . . , N/2; shift-amount setting means for setting a shiftamount mΔf between a desired center frequency of said N-order digitalband pass elliptic filter and a predetermined center frequency f_(r) ;multiplying means for multiplying said shift amount mΔf, supplied fromsaid shift-amount setting means, by each of said linear coefficientsK_(aji) and k_(b1i) to yield mΔf·k_(aji) and mΔf·k_(b1i) ; adding meansfor adding each of products obtained by said multiplying means to anassociated one of said filter coefficients stored in said memory meansto obtain a_(1i) (f_(r))+mΔf·k_(a1i), a_(2i) (f_(r))+mΔf·k_(a2i) andb_(1i) (f_(r))+mΔf·k_(b1i) ; and setting means for setting values a_(1i)(f_(r))+mΔf·k_(a1i), a_(2i) (f_(r))+mΔf·k_(a2i) and b_(1i)(f_(r))+mΔf·k_(b1i) obtained by said adding means as said filtercoefficients {a_(1i), a_(2i), b_(1i) } of said N-order digital band passelliptic filter, thereby setting a center frequency of said N-orderdigital band pass elliptic filter to f_(r) +mΔf.
 2. A center-frequencyvariable type digital band pass filter system comprising:a digital bandpass filter for filtering an input digital signal in accordance with setfilter coefficients; memory means for storing values indicating changeamounts of said filter coefficients with respect to a unit change in apass band center frequency of said band pass digital filter, and filtercoefficients of said band pass digital filter with respect to apredetermined center frequency; difference setting means for setting adifference between a desired center frequency of said band pass digitalfilter and said predetermined center frequency; multiplying means formultiplying said difference, set by said difference setting means, byeach of said values indicating said change amounts; adding means foradding each of results of multiplication by said multiplying means to anassociated one of said filter coefficients with respect to saidpredetermined center frequency; and filter coefficient setting means forsetting results of addition by said adding means as new filtercoefficients of said band pass digital filter.